Welcome aboard Obadiah.

In plain old MTW, you can change which 16 start the battle. In the deployment screen along with the usual buttons is a button with some men on it and a curved arrow - this is a swap button. I can't remember if the button is on the top or bottom of the screen.

If there is a unit in your starting 16 that you want to replace, simply left-click on that unit then click on the swap button. The unit is replaced by the first unit in the reinforcements queue. Keep clicking this button and it will cycle through all the reinforcements. Continue through this until you get the unit you want. Then you can move on to the next unit to replace. This is a bit of a pain compared to VI, but it works. If you really have the patience, you can use this method to control the order of the reinforcement...but I doubt it is worth the effort.